Determining supply curves

Stanford Plastics, Inc. and Cal-Tech Associates, Inc. supply a generic phone jack that connects telephone cords to phone outlets. Proprietary cost and output information for each company reveal the following relations between marginal cost and output:

MCS=dTCS/dQ=$1+$0.00002QS (Stanford)

MCC=dTCC/dQ=$1.50+$0.000005QC (Cal-Tech)

The wholesale market for modular phone jacks is vigorously price-competitive, and neither firm is able to charge a premium for its products. Thus, P = MR in this market.

A. Determine the supply curve for each firm. Express price as a function of quantity and quantity as a function of price. (Hint: Set P = MR = MC to find each firm's supply curve.)
B. Calculate the quantity supplied by each firm at prices of $1, $1.50, and $2. What is the minimum price necessary for each individual firm to supply output?
C. Determine the industry supply curve when P < $1.50.
D. Determine the industry supply curve when P > $1.50. To check your answer, calculate quantity at an industry price of $2 and compare your answer with part B.

Solution Preview

A. Determine the supply curve for each firm. Express price as a function of quantity and quantity as a function of price. (Hint: Set P = MR = MC to find each firm's supply curve.)

For Standard Associates, Marginal cost function is given by
MCS=1+0.00002Qs

Every firm sets its output level such that MR=MC to maximize its profits. In the price competitive industry P=MR.
So, Put P=MC

P=1+0.00002Qs
0.00002Qs=-1+P
Qs=-50000+50000P

For Cal-Tech, Marginal cost function is given by

MCC=1.50 ...

Solution Summary

Solution describes the steps to determine supply curve for the given firms. It also determines the industry supply curves for the given price ranges.